Wide gaps and Kleinberg?s clustering axioms for k-means - Kłopotek, Mieczysław (Zielona Góra: Uniwersytet Zielonogórski)
The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density within/between clusters and is in conflict with Kleinberg`s axiomatic system for distance based clustering algorithms that formalizes those expectations. In particular, k-means violates the consistency axiom. We hypothesise that this clash is due to the unexplained expectation that the data themselves should have the property of being clusterable in order to expect the algorithm clustering them to fit a clustering axiomatic system.
Keywords: clustering theory; clustering axioms; clusterability